Tikhonov方法在不适定模型修正中的应用  

Parameters updating of simulation models with ill-posed characteristics

作　　者：邱飞力[1] 张立民[1] 张卫华[1] 

机构地区：[1]西南交通大学牵引动力国家重点实验室,成都610031

出　　处：《振动与冲击》2015年第12期121-126,145,共7页Journal of Vibration and Shock

摘　　要：数值建模和分析在结构动态设计中应用广泛,为获取准确的计算模型,基于参数灵敏度有限元修正技术得到迅速发展。然而,参数灵敏度矩阵病态性和修正目标函数方程组的不适定性,造成最小二乘直接法难以得到稳定的物理解。为此,对灵敏度矩阵的病态和模型优化方程组的不适定性进行研究,以铁道车辆6自由度离散模型和有限元支架模型为载体,采用Tikhonov正则化方法分别完成了超定系统和欠定系统仿真模型的参数修正。从而,解决了病态不适定系统中最小二乘直接法无稳定物理解的缺陷。参数修正后的模型准确反应了实际结构的尺寸差别和质量,这表明该方法具有实际的应用价值。Along with the wide application of numerical analysis and modeling,getting a correct simulation model becomes an urgent requirement and consequently the parameter-sensitivity updating method has been developed rapidly. The direct least square method can＇t always get the steady physical solution in the cases of ill-posed target function equations and ill-conditioned sensitivity matrixes.The ill characteristics of the sensitivity matrixes and target function equations were investigated.A six-DOF discrete vehicle and a frame finite element model were updated with the Tikhonov regulation method by using the over determined and under determined simulation model respectively.The defect of the direct least square method was solved.The updated models reflect exactly the real mass and the size difference.of the structure.It＇s proved that the method is applicable in engineering practice.

关 键 词：模型修正 参数灵敏度 不适定系统 正则化方法 

分 类 号：TH113.1[机械工程—机械设计及理论] O327[理学—一般力学与力学基础]